Does the shadow clone Assault stack when it moves out and in again in the same combat, because it says give me Assault 4 this turn?

No. The clone's "When I attack" trigger only fires once per combat, even if it leaves and comes back.

Attack triggers are only checked once per combat — gaining and losing the Attacker designation multiple times doesn't re-check them (Rule 383.4.e.2.a). So if the clone moves out and back into the same combat, the second arrival doesn't grant another Assault 4; it keeps only the first one. The "this turn" wording doesn't change that, because it never gets a second trigger to stack with.

The Assault 4 + Assault 4 = Assault 8 lines from the FAQs work because those are two different combats (e.g., conquer one battlefield, Ride the Wind to another). New combat, new trigger check, and the two Assault grants sum per Rule 807.2. Same combat, no re-trigger.